We study of the category O for the queer Lie superalgebra q(n), and the corresponding block decomposition induced by infinitesimal central characters. In particular, we show that the so-called typical blocks correspond to standardly stratified algebras, in the sense of Cline, Parshall and Scott. By standard arguments for Lie algebras, modified to the superalgebra situation, we prove that these ...

In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extensions of g⊗A where g is a basic classical Lie superalgebra and A is Laurent polynomial ring in several variables. The case where g is a simple finite dimensional Lie algebra is included.

Simple modules for the restricted Witt superalgebra W (m,n, 1) are considered. Conditions are provided for the restricted and nonrestricted Kac modules to be simple. Mathematics Subject Classification (2000): 17B50; 17B10.

We introduce the notion of “local system of ZT -twisted vertex operators” on a Z2-graded vector space M , generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of ZT -twisted vertex operators on M has a vertex superalgebra structure with an automorphism σ of order T with M as a σ-twisted module. Then we prove that for a vertex (operator) superal...

We describe a Gauss decomposition for the Yangian Y (glm|n) of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y (A(m− 1, n− 1)) (with m 6= n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians Y (sln|n) and Y (A(n, n)). We also show that the coefficients of the quantum ...

A Gel’fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1, 0, . ....

Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical r-matrices. A super dynamical r-matrix r satisfies the zero weight condition if [h⊗ 1 + 1⊗ h, r(λ)] = 0 for all h ∈ h, λ ∈ h∗. In this paper we explicitly quantize zero-weight super dynamical r-matrices with zero coupling constant for the Lie superalgebra gl(m,n). We also answer some quest...